Kernel Methods for Dependence and Causality

Lecture slides:

• Covariance on RKHS
• Two Views on Kernel Methods
• Covariance on RKHS
• Cross-covariance operator
• Intuition
• Addendum on “operator”
• Characterization of Independence
• Measures for Dependence
• Norms of operators
• Empirical Estimation
• Empirical cross-covariance operator
• COCO Revisited
• HSIC Revisited
• Application of HSIC to ICA
• ICA with HSIC
• Experiments (speech signal)
• Normalized Covariance
• HSIC Revisited
• Nonlinear dependence

Author: Kenji Fukumizu, Institute of Statistical Mathematics